Source: Magoosh
Two teachers, Ms. Ames and Mr. Betancourt, each had N cookies. Ms. Ames was able to give the same number of cookies to each one of her 24 students, with none left over. Mr. Betancourt also able to give the same number of cookies to each one of his 18 students, with none left over. What is the value of N?
1) N < 100
2) N > 50
The OA is A.
Two teachers, Ms. Ames and Mr. Betancourt, each had N
This topic has expert replies
-
- Moderator
- Posts: 2209
- Joined: Sun Oct 15, 2017 1:50 pm
- Followed by:6 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
$$\left\{ \matrix{BTGmoderatorLU wrote:Source: Magoosh
Two teachers, Ms. Ames and Mr. Betancourt, each had N cookies. Ms. Ames was able to give the same number of cookies to each one of her 24 students, with none left over. Mr. Betancourt also able to give the same number of cookies to each one of his 18 students, with none left over. What is the value of N?
1) N < 100
2) N > 50
\left( {{\rm{Ames}}} \right)\,\,N = 24 \cdot Q\,\,,\,\,Q \ge 1\,\,{\mathop{\rm int}} \hfill \cr
\left( {{\rm{Betan}}} \right)\,\,N = 18 \cdot K\,\,,\,\,K \ge 1\,\,{\mathop{\rm int}} \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,N = LCM\left( {24,18} \right) \cdot J\,\,,\,\,J \ge 1\,\,{\mathop{\rm int}} $$
(N is a multiple of 18 and also a multiple of 24, hence N must be a multiple of the LCM of 18 and 24.)
$$LCM\left( {{2^3} \cdot 3,2 \cdot {3^2}} \right) = {2^3} \cdot {3^2} = 72\,\,\,\,\,\,\,\, \Rightarrow \,\,\,N = 72 \cdot J\,\,,\,\,J \ge 1\,\,{\mathop{\rm int}} $$
$$? = N$$
$$\left( 1 \right)\,\,N < 100\,\,\,\,\, \Rightarrow \,\,\,\,J = 1\,\,\,\, \Rightarrow \,\,\,\,? = 72$$
$$\left( 2 \right)\,\,N > 50\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,J = 1\,\,\,\, \Rightarrow \,\,\,\,? = 72 \hfill \cr
\,{\rm{Take}}\,\,J = 2\,\,\,\, \Rightarrow \,\,\,\,? = 144 \hfill \cr} \right.$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
As per the information, we have N is a multiple of 24 and 18.BTGmoderatorLU wrote:Source: Magoosh
Two teachers, Ms. Ames and Mr. Betancourt, each had N cookies. Ms. Ames was able to give the same number of cookies to each one of her 24 students, with none left over. Mr. Betancourt also able to give the same number of cookies to each one of his 18 students, with none left over. What is the value of N?
1) N < 100
2) N > 50
The OA is A.
Say,
N/24 = p, where p is a positive integer; => N = 24p
N/18 = p, where q is a positive integer; => N = 18q
=> 24p = 18q
4p = 3q
=> p = 3q/4 => q must be a multiple of 4
q: {4, 8, 12, 16, 20, ...}
Thus, the corresponding values of N are: {72, 144, 288, 360, ...}
If we get the unique value of p or q, we get the answer.
Let's take each statement one by one.
1) N < 100
From the set for N: {72, 144, 288, 360, ...}, we have N = 72. Sufficient.
2) N > 50
From the set for N: {72, 144, 288, 360, ...}, we have {72, 144, 288, 360, ...}. No uniue value of N. Insufficient.
The correct answer: A
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations: Manhattan Review India | Himayatnagar GMAT Coaching | Dilsukhnagar GMAT Courses | Manhattan Review Hyderabad | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Since the N cookies can be divided evenly among 24 or 18 students, N must be divisible by both 24 and 18.BTGmoderatorLU wrote:Source: Magoosh
Two teachers, Ms. Ames and Mr. Betancourt, each had N cookies. Ms. Ames was able to give the same number of cookies to each one of her 24 students, with none left over. Mr. Betancourt also able to give the same number of cookies to each one of his 18 students, with none left over. What is the value of N?
1) N < 100
2) N > 5.
One way to determine the LCM of two integers is to take multiples of the LARGER integer until we get a multiple of the SMALLER integer.
Multiples of 24:
24, 48, 72...
We can stop here: the value in blue is divisible by 18, since 72/18 = 4.
Thus, the LCM of 24 and 18 = 72.
Implication:
Since the N cookies can be divided evenly among 24 or 18 students, N must be a positive MULTIPLE OF 72.
Statement 1: N < 100
Thus, N=72.
SUFFICIENT.
Statement 2: N > 50
Here, N can be any positive multiple of 72.
INSUFFICIENT.
The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3